Why warm up? What does it do for you? What does it mean to you?
I see my warm up almost like a meditation. It's a way of reconnecting my mind with my body and my instrument. I reconnect with the sound I want to make and focus on the physical and mental discipline that I wish to instill in my playing.
In practical terms the length of warm up depends on varying factors. If I have a whole free day ahead of me and can afford a long warm up I will take my time and cover many exercises. But sometimes as a busy working musician, with a family, traveling to a rehearsal or performance rules out the luxury of a long warm up. Therefore I think it's important to be able to warm up in 10/15 minutes and still be able to be at peak performance. Students should practice some days with a long elongated warm up and other days with a short warm up. Vary the length from day to day, vary the exercises and most importantly create your own exercises that address your needs as a brass player.
Here is a short video from a group warm up session at my summer trombone camp.